Chapter 7 notes-Quantum Mechanics: Light, Waves, and Why Electrons are Weird
7.1 Schrodinger’s Cat:
There was a famous thought experiment about a cat in a box. Read about it in Section 7.1, or watch
one of these videos:
http://www.youtube.com/watch?v=uWMTOrux0LM (skip to 0:55)
http://www.youtube.com/watch?v=IOYyCHGWJq4 (neat drawings)
Chapter 7 is weird, it deals with really small things like electrons:
“Things on a small scale behave like nothing you have any direct experience about.
They do not behave like waves.
They do not behave like particles.
They do not behave like clouds or billiard balls or weights on springs or like anything you
have ever seen.”
(Richard Feynman, famous physicist).
7.2 Waves, light, and similar types of energy
Waves have 5 important properties
1. ______________________________________, symbol _____
2. ______________________________________, symbol _____
This is the # of cycles that pass a point in one second,
3. ______________________________________, symbol _____
4. ______________________________________, symbol _____
5. ______________________________________, symbol _____
Unit of ________ or __________
speed of light = ______________________
Energy per photon = ___________________
Speed of light in a vacuum: _______________________________
Evaluate the figures:
Which wave has the:
longest wavelength?
highest frequency?
largest amplitude?
fastest speed?
Figure 7.2
Animation of wave properties: http://www.micro.magnet.fsu.edu/primer/java/electromagnetic/index.html
Energy:
Energy:
Figure 7.5: Evaluate the figure: which has higher Energy, gamma or radio?
Calculations
1. What is the wavelength of light that has a ν of 7.95×1014 s–1?
2. What is the ν of light with λ = 3.33 m
3. Which is more energetic?
a) 585 nm light
b) 2.22 x 1014 s-1 light
Waves or Particles?
Properties of waves: interference
Draw result of interference:
(use proper units!)
Interference: When waves combine constructively or destructively
Photoelectric effect:
The Photoelectric Effect:
Light can act as a _________________________________________or a _____________________________________________
If you can figure this experiment out, let me know: http://phys.org/news/2015-03-particle.html
Quantized Energy:
Max Planck, in 1900, claims that objects absorb or release energy in discrete packets called:
__________________
For particles, Planck describes that the energy absorbed or released is equal
to a constant times the frequency of energy emitted. The equation is: ________________________________
h is Planck’s constant __________________________________
Einstein (1905) claims that light travels in individual packets called ___________________________, which
are single wave pulses of energy.
One photon has _________________________________ energy, _______________________ for visible photons
The energy of one photon has the equation:
Ephoton = _______________________________
Quantized energy is like positions on stairs vs. a ramp. Circle the one that provides quantized
positions.
Calculations:
3. What is the energy of light that has a ν of 7.95 x 1014 s–1?
4. What is the energy of light with λ = 3.33 m?
5. What is the total energy available in 1.50×1024 photons with a ν of 7.95 x 1014 s-1
Review example 7.2!
NOTE: Formula is for E of one photon. Chemical reactions require one photon per bond broken
Atomic Spectroscopy, or how do physicists explain line spectra?
White light, like from the sun or a light bulb, has many wavelengths and is ____________________________.
Elements discharge light that consists of few wavelengths, called ____________________________________.
Colors are emitted from excited atoms when electrons _____________________________________________
The Rydberg equation, where n = 1, 2, 3, 4, ……..
Simple whole numbers allow the calculation of emission wavelengths.
R
= H
λ  h
1
1 
 1
 2 − 2 
 n1 n2 
The original Heisenberg, Particles and Wavelengths
The Bohr Model, an attempt to explain line spectra
• Bohr (Denmark): e– travel in _______________________________________________
•
•
Light emitted when e– move from ___________________________________________
Explained why Energy emitted from excited atoms is ______________________
The Bohr model is limited in that it works
________________________________________________________________________________________
h
Louis De Broglie suggests that all particles have wavelengths: λ = mv
•
mv is a particle property (mass x velocity),
•
How can this be? Electrons act like waves or particles
• (read QED by Feynman) or read http://www.wired.com/2014/09/double-slit-empzeal/
The Heisenberg Uncertainty Principle,
For electrons, the __________________________________________ and _____________________________________________
can’t be determined precisely in the same moment.
Δx = uncertainty in position
Δmv = uncertainty in momentum (mass * velocity)
∆x·∆mv ≥
h
4π
Watch some interesting slides about the uncertainty principle, which is important for only with
_____________________ particles.
How to reconcile electrons being like waves and particles, or back to explaining line spectra:
Enter Erwin Schrödinger, published papers in 1926 describing wave mechanics and an equation to
calculate emission energies. The equation has:
1. both _____________________________ and __________________________________ terms.
2. leads to __________________________________________ ψ “psi”
3. gives the __________________________________________ and _________________________________ for an atom.
4. Allows for __________________________________________________________ (Bohr model didn’t)
Schrodinger wrote one of the most significant set of physics papers (4) in history.
Figure 7.22, electron density
What that crazy equation calculates:
probability distribution
Wave functions from Schrödinger’s equation allow the calculation of
1. Energy levels for e–
2. Space where e– located, called orbitals.
3. Each orbital holds 0, 1 or 2 e– (don’t confuse with Bohr’s orbits)
Schrödinger’s eq needs _____________________________________________________________
1. Principal Quantum Number, __________________________.
same as Bohr’s ___________________
larger n = ____________________________________________
larger n means e– can be __________________________________________________
2. Azimuthal (shape) ______
Chemists use ______________________________________ orbital names to describe shapes.
3. Magnetic (orientation) __________ __________________________________________________________________
4. Spin ____________
electrons spin in ___________________________ different ways
Shapes of orbitals and nodes
•
•
•
All ______________________________________________________________
get larger as n increases.
Each s orbital can hold either ________________________________________________________________
A node is where the probability of finding an electron is zero
•
•
Electrons travel in waves (in some experiments)
Wave on right has two phases, just like electrons in 2s or 2p
orbitals
A node is where the ________________________________________________________________________________________
There are ___________________________________, each with _____________________________ for a total of __________
per energy level